Statistical and systematic uncertainties

For each process, the statistical uncertainty on the estimation has been calculated combining the uncertainties from each component of equation4.1: data in CR and MC in both SR and CR. In order to calculate the statistical error on the total Z/W+jets BG the uncertainties of all the processes are combined, taking into account the correlations.

Different classes of systematic uncertainty are considered in the Z/W+jets BG de-termination:

• Z/W+jets MC modeling

• Jet andE_T^miss related uncertainties

• Lepton identification

• Background subtraction in control regions

• Trigger efficiency

• Luminosity

Uncertainties on the Z/W+jets MC modeling As we discussed previously, the data-driven method implemented in this BG estimation allows to cancel the leading contribution of the different sources of uncertainty on the MC simulation. In the following, the residual uncertainties on the Z/W+jets MC prediction are assessed. This includes uncertainties related to: parton shower (PS) modeling, matrix element to PS matching, choice of the renormalization and factorization scales, and the choice of the PDF set. The different variations result in different predictions for the processes under study. For example, on the Z+jet and W+jet production ALPGEN and SHERPA give different predictions, in particular on the shape of the jet p_T. Figures 4.12(a) (taken from [92] ) and 4.12(b) (taken from [93]) show the measured differential cross section as a function of the leading jet pT inZ(→//)+jets andW(→/ν)+jets events, respectively. Considering the systematic uncertainties on these measurements both the ALPGEN and SHERPA predictions are in agreement with the data. Nevertheless, the shape the jetp_T in the two MCs has opposite tendency. At p_T ∼150 GeV ALPGEN and SHERPA predictions differ by∼20% and the difference tends to increase for higher p_T.

50 100 150 200 250 300

Figure 4.12: Differential cross section measurement of Z(→//) +jets (left) and W(→ /ν) +jets (right) as a function of leading jet p^T. Pictures are taken from [? ] and [? ] references. Integrated luminosities of 5 fb⁻¹ and 35 pb⁻¹ of 7 TeV data have been used respectively for the left and right plot. The measured differential cross section is compared with predictions from SHERPA and ALPGEN, showing a different behavior of the two MC generator on the jetp^T prediction.

To assess systematic uncertainties on the MC modeling, the Z/W+jets BG estima-tions made with ALPGEN and SHERPA have been compared. Because of the large difference between the two MC predictions, this is considered a conservative approach.

Two different procedures have been carried out for comparing ALPGEN and SHERPA results. The first compares directly the estimations made with the two sets of MC samples, resulting in SR1 in a difference of 1.6% with a statistical error of 1.1%. For SR2, SR3 and SR4 the differences are 3.7±3.0%, 8±11% and 4±26%. Due to the severe lack of statistics in the SHERPA samples the comparison suffers from large un-certainties as one increases theE_T^miss and jetp_T thresholds. In the second comparison,

the ALPGEN events have been re-weighted to follow thep_T distribution of the W and Z bosons in SHERPA. The weights are defined by the ratio of the distributions in the two sets of MC samples before any selection is applied. The values of the weights go from 1.15 at low boson p_T, to 0.72 for p_T > 250 GeV. The comparison between the original ALPGEN predictions and the predictions from the modified samples is about 3% in SR1 and is smaller than 1% for the other SRs.

The ALPGEN-SHERPA differences from these two comparisons are summarized in figure 5.5. The difference shows no dependency with increased thresholds on p_T and E_T^miss. Therefore an uncertainty of 3% has been considered for the four SRs.

SR1 SR2 SR3 SR4

relative difference in %

-10 -5 0 5 10 15 20

Sherpa Vs AlpGen

AlpGen(weighted) Vs AlpGen

Figure 4.13: Detail of the comparison between the total Z/W+jets BG using SHERPA and ALPGEN MC samples. Black points show the relative difference between the SHERPA and ALPGEN estimations. Blue points show the relative change of the ALPGEN results when weights have been applied to correct the bosonp^Tdistribution based on the SHERPA prediction. Based on these result a systematic uncertainty of 3% has been chosen (repre-sented by the shadowed band).

Lepton related uncertainties The uncertainty on the lepton identification is not reduced by the data-driven BG estimation, because its effects are not canceled in the TF ratios. Nevertheless, MC events are corrected with lepton identification scale factors to

have the same reconstruction efficiency as in data, and the remaining uncertainties are propagated to the final result. The uncertainty on the scale factors are both statistical (from the finite size of the event sample used to estimate them) and systematics (from the method implemented to retrieve them).

In the case of the muon scale factors, this translates into uncertainties between a 0.8% and 3% on the total BG as the jet p_T and E_T^miss increase. Similarly, the uncertainty on the electron scale factors introduces an uncertainty on the total BG that varies between 0.4% and 0.3%. The effect of the electron systematics is smaller compared to the muon, because the electron CR is used only for the W(→ eν) +jet and Z(→τ τ) +jet estimations. The uncertainties on the muon momentum scale and resolution have been evaluated and varies between 0.02% for SR1 and 0.5% for SR4.

Instead, the uncertainties on the electron energy scale goes from 0.2% for SR1 and 0.3%

for SR4. The final systematic uncertainty due to the lepton identification (considering both electrons and muons) is 1% and 3% for SR1 and SR4, respectively.

Jet and E^miss_T related uncertainties Various sources of systematic uncertainties on the jet energy scale (JES) have been considered[65]: calorimeter energy response, MC-based and in-situ calibration, pile-up and presence of close-by jets, partonic flavor, are the most relevant (see section 3.3.3). The JES uncertainty, in absence of pile-up and near-by jets, varies between 2.5% for central high-p_T jets (|η| < 0.8, 60 < p_T <

800 GeV) and 14% for forward low-p_T jets (3.2 < |η| < 4.5, 20 < p_T < 30 GeV).

Close-by jets with∆ R < 0.7 introduce an additional uncertainty of 2-3%. Multiple interactions in the same bunch-crossings introduce, for jets with p_T = 30 GeV (p_T = 100 GeV), an uncertainty on the jet momentum of 0.5% (0.1%) for each reconstructed vertex. To evaluate the impact on the Z/W+jets BG estimation, the p_T of all jets is scaled up and down according to the JES uncertainty, and the estimation is repeated.

The impact due to the jet energy resolution (JER) uncertainty has been evaluated by smearing the p_T of all the jets according to the its uncertainty. The effect of JER on the total BG estimation is negligible.

The E_T^miss reconstruction has various sources of uncertainties due to the presence of jets, electrons, and soft particles coming from pile-up and underlying event. No uncertainty needs to be estimated regarding the muons since the muons are not part of the E_T^miss reconstruction.

The main E_T^miss uncertainty is related to the JES, and is evaluated varying simul-taneously the E_T^miss and thepT of the jets since their uncertainties are correlated. To estimate the impact of the JES on theE_T^miss, the relative jet-level variations of the first two leading jets are propagated to theE_T^miss. As a cross-check the same procedure has been carried out considering all jets with p_T >20 GeV for the E_T^miss estimator. The first procedure gives larger uncertainties and it has been used for the final results in table4.3. The total uncertainty due toE_T^missand JES on the final number of BG events in the signal region is about 2% for SR1. It is worth mentioning that the Monte Carlo predictions in the SR and the CR both move byO(20%). Thus the 2% is the residual uncertainty after applying the TF method. In SR4 the uncertainty increases up to 4%

reflecting, to some extent, the limited MC statistics.

TheE_T^missuncertainty from the electron energy scale has been estimated by varying the electronp_Taccording to its uncertainty, and simultaneously propagating the change to theE_T^miss. The effect on the total Z/W+jets estimation is 0.2% in SR1.

As the E_T^miss is computed using all topo-clusters up to |η|<4.5, and not only the ones associated with jets or electrons, the uncertainty from non associated topo-clusters needs to be evaluated. This is done by changing the topo-cluster energy scale according to the E/p studies carried out in ATLAS. The effect of this component on the transfer factors is negligible.

Uncertainties from background subtraction in control regions In the lepton control regions there is a small contribution from the tt, single top and di-bosons.¯ These processes are subtracted from the CRs using MC estimates. The uncertainty on the subtraction propagates as an uncertainty on the number of data events in the CR, which leads to an uncertainty on the Z/W+jets BG determination in the SR.

A conservative 20% uncertainty is considered on the number of t¯t, single top and di-bosons. The uncertainty on these processes is considered fully correlated, because the JES uncertainty (about 16%) is the dominant uncertainty on these BGs. This subtraction results in about 1% uncertainty on the Z/W+jets BG in the SRs.

Uncertainty on the luminosity The uncertainty on the absolute integrated lu-minosity is not considered for the final result since it affects the numerator and the

denominator of the TF in the same way, so that the ratio is unchanged. The lumi-nosity uncertainty on top and di-boson production indirectly affects the Z/W+jets estimation. This effect is very small and is considered in the uncertainty on the BG subtraction in the CRs.

Uncertainties on the trigger efficiency As described in section 4.4, the trigger used for this analysis is ∼ 98% efficient for SR1 and a ∼ 1% difference in efficiency between data and MC has been observed. Instead, for SR2, SR3, and SR4 the trigger selection is fully efficient. In order to evaluate the effect of the trigger turn-on curve, the full Z/W estimation has been repeated with different trigger requirements on MC events. In one case a trigger item with higher thresholds (“EF xe90 noMu”) has been used, and in another case no trigger requirement have been made. This test shows how much the BG estimation can vary when using a very different trigger efficiency in the MC. Differences on the total Z/W+jets BG are 0.2% at most.

Summary of the uncertainties Table4.3summarizes the systematic uncertainties on the total Z/W+jets predictions. The final BG estimation uses the combination of the results from W(→ µν) and Z(→ µµ) CRs to estimate Z(→ νν), W(→ τ ν), W(→µν) andZ(→µµ) processes.

As stated previously, these processes could be also estimated from the inclusive muon CR. Table 4.3presents the systematic uncertainties on the BG estimation when predicting these processes from either the inclusive muon CR, or theW(→µν) CR, or the combination of W(→µν) and Z(→ µµ) CRs. The results show how the system-atic uncertainties are at the same level for different definitions of the CRs. Table 4.3 shows also that predictions using the inclusive muon CR have slightly lower systematic uncertainties compared to those from the other CRs, especially for SR1 and SR2. This is explained by the fact that the cuts on M_T in theW(→µν) CR, and onM_µµ in the Z(→µµ) CR introduce a further difference between SR and CR selections. Previously it has been explained that the systematic uncertainties are largely reduced because they affect the TF numerator and denominator in the same (or similar) way, so that the ra-tio is much less sensitive to systematic effects. Therefore, if further selecra-tion criteria are added in the CRs and not in the SR, the systematic uncertainties are bounded to increase.

Inclusive muon CR

Systematics Region 1 Region 2 Region 3 Region 4

MC modeling 3.0% 3.0% 3.0% 3.0%

E_T^miss/JES/JER 1.5% 2.7% 3.7% 4.0%

Lepton id./scale/res. 0.8% 1.5% 1.8% 2.7%

Background subtraction 1.0% 0.8% 0.8% 1.1%

Trigger 0.2% - -

-Luminosity - - -

-Exclusive W(→µν) CR

Systematics Region 1 Region 2 Region 3 Region 4

MC modeling 3.0 % 3.0% 3.0% 3.0%

E_T^miss/JES/JER 2.2% 3.4% 3.8% 2.6%

Lepton id./scale/res. 0.7% 1.1% 1.4% 2.4%

Background subtraction 1.1% 0.9% 1.0% 1.2%

Trigger 0.2% - -

-Luminosity - - -

-Combined results from W(→µν) andZ(→µµ) CRs

Systematics Region 1 Region 2 Region 3 Region 4

MC modeling 3.0 % 3.0% 3.0% 3.0%

E_T^miss/JES/JER 2.1 % 2.9% 3.9% 2.1%

Lepton id./scale/res. 0.7 % 1.1% 1.4% 2.4%

Background subtraction 1.1 % 0.9% 0.9% 1.1%

Trigger 0.2% - -

-Luminosity - - -

-Table 4.3: Summary of the systematic uncertainties on the total Z/W+jets background.

The final uncertainties are compared for different choices of the muon CRs: the inclusive muon CR, theW(→µν) CR, the combination of bothW(→µν) andZ(→µµ) CRs